Fixed Boundaries Influence in Biological Networks: From Theory to Application

Abstract. The purpose of this paper is to present some results about the influence of fixed boundary conditions in biological regulation networks. More precisely, we will present theoretical and simulation results in the context of theoretical connected regulation networks on Zd. These re-sults will show under which conditions phase transitions emerge from the asymptotic behaviour of such networks when they are subjected to the influence of fixed boundaries. Furthermore, we will expose some math-ematical results obtained on the regulation network of the floral mor-phogenesis of the plant Arabidopsis thaliana that explain experimental results on the necessary presence of a Gibberellin hormone for the plant to develop normally